A new finite‐element shell model for arterial growth and remodeling after stent implantation

Abstract

The goal of this paper is to study computationally how blood vessels adapt when they are exposed to a mechanobiological insult, namely, a sudden change of their biomechanical conditions such as proteolytic injuries or implantation.Adaptation occurs through growth and remodeling (G&R), consisting of mass production or removal of structural proteins, such as collagen, until restoring the initial homeostatic biomechanical conditions. In some circumstances, the initial conditions can never be recovered, and arteries evolve towards unstable pathological conditions, such as aneurysms, which are responsible for significant morbidity and mortality. Therefore, computational predictions of G&R under different circumstances can be helpful in understanding fundamentally how arterial pathologies progress. For that, we have developed a low-cost open-source finite-element 2D axisymmetric shell model (FEM) of the arterial wall. The constitutive equations for static equilibrium used to model the stress-strain behavior and the G&R response are expressed within the homogenized constrained mixture theory. The originality is to integrate the layer-specific behavior of both arterial layers (media and adventitia) into the model. Considering different mechanobiological insults, our results show that the resulting arterial dilatation is strongly correlated with the media thickness. The adaptation to stent implantation is particularly interesting. For large stent oversizing ratios, the artery cannot recover from the mechanobiological insult and dilates forever, whereas dilatation stabilizes after a transient period for more moderate oversizing ratios. We also show that stent implantation induces a different response in an aneurysm or in a healthy artery, the latter yielding more unstable G&R. Finally, our G&R model can efficiently predict, with very low computational cost, fundamental aspects of arterial adaptation induced by clinical procedures. KEYWORDSarterial growth and remodeling, axisymmetric shell model, homogenized constrained mixture theory, layer-specific behavior, stent implantation Int J Numer Meth Biomed Engng. 2020;36:e3282.wileyonlinelibrary.com/journal/cnm

Fast, rate-independent, finite element implementation of a 3D constrained mixture model of soft tissue growth and remodeling

“…Note that the computational efficiency of this rate-independent G&R formulation is comparable to that obtained for hyperelastic computations, for which we used the same mesh, boundary conditions, applied loads, and incremental steps along with Eqs. (49) and (50), and, hence, is expected to be comparable as well to that obtained by efficient rate-dependent G&R formulations (e.g., in 2D FE analyses [37]). Lastly, because mechanobiologically equilibrated G&R is not constrained isochorically (recall Remark 1), no special formulations were needed to prevent volumetric locking during these computations, a numerical issue characteristic of nearly incompressible elastic or distortional elastoplastic responses [24,38], but also transient elastic responses during G&R [36,39].…”

A nonlinear rotation-free shell formulation with prestressing for vascular biomechanics

“…Including CMT in future fluid-solid simulations will extend our prior work 58 to subject-specific geometries and large displacements and thereby improve the understanding of the interplay between altered hemodynamics and vascular adaptation. Since the current shell formulation is based only on displacement degrees of freedom, it also enables standard integration with the methodologies proposed in literature to perform acute stress analysis on stents 59 , to investigate vascular adaptation following the stent implantation 60 , and indeed to consider a host of clinical interventions for patient-specific geometries.…”

Patient‐specific computational modeling of endovascular aneurysm repair: State of the art and future directions

“…In the last two decades, collagen fiber dispersion has been included into the models as a key contributor to the mechanical response of the aortic wall 75–78 . AAA progression is usually associated with a loss of elastin 72,125 as well as structural changes of the elastin and collagen fiber network 72,156 with increased fiber dispersion 17,57 leading to a more isotropic behavior. Thus simplified isotropic models are widely used for AAA wall modeling 63,72,136 .…”

“…Numerical models can be an interesting alternative option for studying influencing factors in sac expansion/shrinkage. Only one numerical model has ever been published on aneurysm adaptation after EVAR 156 . In that original study, a 2D finite‐element axisymmetric shell model was developed for simulating G&R after stent‐graft implantation.…”